The zero-determinant (ZD) strategy provides a new perspective for describing the interaction between players, and the errors among them will be an important role in designing ZD strategy, which attracts a lot of researches in various fields. This paper investigates how to design ZD strategy for multiplayer two-strategy repeated finite game under implementation errors. First, the implementation errors

The secret behind cooperation with the present profit-pursuing nature has been unveiled via the Evolutionary Game Theory and models. However, the payoff equality is not sufficiently explored. This paper proposes a simple but efficient way to focus on the synergetic behaviors of payoff equality and cooperation improvement. Herein, the classical Evolutional Game model is re-evaluated from the perspective

In this paper, a stochastic tumor–immune model with comprehensive pulsed therapy is established by taking stochastic perturbation and pulsed effect into account. Some properties of the model solutions are given in the form of the Theorems. Firstly, we obtain the equivalent solutions of the tumor–immune system by through three auxiliary equations, and prove the system solutions are existent, positive

The goal of this work is to propose a new type of constraint for linear programs: inequalities having infinite, finite, and infinitesimal values in the right-hand side. Because of the nature of such constraints, the feasible region polyhedron becomes more complex, since its vertices can be represented by non-purely finite coordinates, and so is the optimum of the problem. The introduction of such constraints

In real life, a good reputation generally brings positive returns to individuals. For example, merchants with numerous good reviews usually gain higher profits. Considering this in the ultimatum game, we propose a reputation-based reward mechanism to investigate the evolution of fairness. Specifically, individuals' reputations evolve dynamically based on the outcomes of games. At the same time, we

In this work, we consider and analyze explicit exponential Runge–Kutta methods for solving semilinear time-fractional integro-differential equation, which involves two nonlocal terms in time. Firstly, the temporal Runge–Kutta discretizations follow the idea of exponential integrators. Subsequently, we utilize the spectral Galerkin method to introduce a fully discrete scheme. Then, we mainly focus on

This paper is mainly concerned with introducing a numerical method for solving initial–boundary value problems with integer and fractional order time derivatives. The method is based on discretizing the considered problems with respect to spatial and temporal domains. With the help of finite difference methods, we transformed the studied problem into a set of fractional differential equations. Then

In this article, based on the grad-div stabilization, we propose a generalized scalar auxiliary variable approach for solving a fluid–fluid interaction problem governed by the Navier–Stokes-/Navier–Stokes- equations. We adopt the backward Euler scheme and mixed finite element approximation for temporal-spatial discretization, and explicit treatment for the interface terms and nonlinear terms. The proposed

The influence of algal cell size on nutrient absorption, and the time delay in reproduction is paramount in biological terms. Furthermore, the control is necessary during algal flocculation harvesting and sewage treatment. Therefore, we investigated the properties of a single cell algal flocculation model with time delay, size structure and control. First, we introduced a dimensionless model. Then

Using the -dressing method, we study the general reverse-space nonlocal nonlinear Schrödinger (nNLS) equation. Beginning with a 3 × 3 matrix -problem, the associated spatial and time spectral problems are obtained through two linear constraint equations. Furthermore, the gauge equivalence between the Heisenberg chain equation and the general reverse-space nNLS equation is established. By employing

The harmonic numbers and higher-order harmonic numbers appear frequently in several areas which are related to combinatorial identities, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this paper is to study the degenerate harmonic and degenerate higher-order harmonic numbers, which are respectively degenerate versions of the harmonic and

This paper introduces a novel temporal second-order fully discrete approach of finite element method (FEM) and its fast two-grid FEM on non-uniform meshes, which aims to solve non-linear time-fractional variable coefficient mobile/immobile (MIM) equations with a solution exhibiting weak regularity. The proposed method utilizes the averaged L1 formula on graded meshes in the temporal domain to handle

The Functional Quantization (FQ) method was developed for the approximation of random processes with optimally constructed finite sets of deterministic functions (quanta) and associated probability masses. The quanta and the corresponding probability masses are collectively called a “”. A method called “Functional Quantization by Infinite-Dimensional Centroidal Voronoi Tessellation” (FQ-IDCVT) was

In this paper, we propose nonlinear conjugate gradient methods for vector optimization on Riemannian manifolds. The concepts of Wolfe and Zoutendjik conditions are extended to Riemannian manifolds. Specifically, the existence of intervals of step sizes that satisfy the Wolfe conditions is established. The convergence analysis covers the vector extensions of the Fletcher–Reeves, conjugate descent, and

In this work, we present a conservative Allen–Cahn (CAC) equation and investigate its unconditionally maximum principle-preserving linear numerical scheme. The operator splitting strategy is adopted to split the CAC model into a conventional AC equation and a mass correction equation. The standard finite difference method is used to discretize the equations in space. In the first step, the temporal

In this paper, we introduce a novel Gauss–Jacobi quadrature rule designed for infinite intervals, which is specifically applied to the velocity discretization in multi-scale Boltzmann solvers. Our method utilizes a newly formulated bell-shaped weight function for numerical integration. We establish the relationship between this new quadrature and the classical Gauss–Jacobi, as well as the Gauss–Hermite

An innovative simultaneous space–time Hermite wavelet method has been developed to solve weakly singular fractional-order nonlinear integro-partial differential equations in one and two dimensions with a focus whose solutions are intermittent in both space and time. The proposed method is based on multi-dimensional Hermite wavelets and the quasilinearization technique. The simultaneous space–time approach

In this paper, we employ the Lyapunov theory to generalize the finite time stability (FTS) results from general deterministic impulsive systems to impulsive stochastic time-varying systems, which overcomes inherent challenges. Sufficient conditions for the FTS of the system under stabilizing and destabilizing impulses are established by using the method of average dwell interval (ADT). For FTS of stabilizing

We study the bifurcation behavior of nodal solutions for the Kirchhoff type beam equation where is a parameter, and are smooth functions. We obtain the existence of nodal solutions under some suitable conditions. The proof of our main result is based upon bifurcation techniques.

This paper provides an improved exponential growth estimate, surpassing the growth rate given in the previous work. This finding elucidates the impact of the power index in the logarithmic nonlinearity on the growth behavior of the solution to the initial boundary value problem for the one-dimensional sixth-order nonlinear Boussinesq equation with logarithmic nonlinearity.

Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than 1 are derived. An application in coding theory is illustrated by showing that multispace codes that are introduced here may be used in random linear network coding scenarios, and that they generalize standard subspace codes (defined in the set of all subspaces

In this paper, we introduce novel analytical solutions for valuating volatility derivatives, including volatility options and capped/floored volatility swaps, employing discrete sampling within the framework of the Merton jump-diffusion model, which is driven by a nonhomogeneous Poisson process. The absence of a comprehensive understanding of the probability distribution characterizing the realized

This paper studies the adaptive distributed unknown input observer (ADUIO) for linear systems with local outputs, which contains a group of local observers under directed graph. The difficulty is the adaptive estimation of global output for the systems with unknown inputs. To solve the problem, disturbance decoupling principle and leader-following consensus strategy are integrated to estimate local

In this paper, we introduce a new sliding mode observer for Lur’e set-valued dynamical systems, particularly addressing challenges posed by uncertainties not within the standard range of observation. Traditionally, most ofLuenberger-like observers and sliding mode observer have been designed only for uncertainties in the range of observation. Central to our approach is the treatment of the uncertainty

The fractional material derivative appears as the fractional operator that governs the dynamics of the scaling limits of Lévy walks - a stochastic process that originates from the famous continuous-time random walks. It is usually defined as the Fourier–Laplace multiplier, therefore, it can be thought of as a pseudo-differential operator. In this paper, we show that there exists a local representation

Energy harvesters for mechanical vibrations are electro-mechanical systems designed to capture ambient dispersed kinetic energy, and to convert it into usable electrical power. The random nature of mechanical vibrations, combined with the intrinsic non-linearity of the harvester, implies that long, time domain Monte-Carlo simulations are required to assess the device performance, making the analysis

In this paper, we study the uniqueness of the stationary sonic–subsonic solution to the isentropic hydrodynamic model of semiconductors with sonic boundary. We provide a new method to improve the proof of the uniqueness of the steady-state sonic–subsonic solution, even for the general isentropic case. In detail, we apply the exponential variation method combining a series of modifications with respect

In this letter we report a new type of multi-soliton solutions for the modified Korteweg–de Vries (mKdV) equation. These solutions contain functions of the trigonometric solitons and classical solitons simultaneously. A new bilinear form of the mKdV equation is introduced to derive these solutions. The obtained solutions display as solitons living on a periodic background, which are analyzed and illustrated

In this paper, a data-driven method is employed to investigate the probability density function (PDF) of nonlinear stochastic ship roll motion. The mathematical model of ship roll motion comprises a linear term with cubic damping and a nonlinear restoring moment represented as an odd-degree polynomial up to the fifth order. The data-driven method integrates maximum entropy, the pseudo-inverse algorithm

This paper addresses the input-to-state formation stabilization problem of nonlinear multi-agent systems within a hybrid impulsive framework, considering delay-dependent impulses, strong nonlinearity, and deception attack signals. By leveraging Lyapunov functionals, impulsive comparison theory, average impulsive interval methods, and graph theory, we develop novel criteria for possessing locally input-to-state

The parallel row ordering problem (PROP) is concerned with arranging two groups of facilities along two parallel lines with the goal of minimizing the sum of the flow cost-weighted distances between the pairs of facilities. As the main result of this paper, we show that the insertion neighborhood for the PROP can be explored in optimal time by providing an -time procedure for performing this task,

This paper studies the stability problem of switched systems with state-dependent delayed impulses (SDDIs), where switching times satisfy the definition of average dwell-time. Firstly, the pulse phenomenon of the systems with SDDIs is avoided under some necessary assumptions. Subsequently, the state-dependent delayed impulsive switched systems can be transformed into the corresponding time-dependent

In the framework of perturbed Keplerian systems we deal with the Delaunay normalisation of a wide class of perturbations such that the radial distance is raised to an arbitrary real number . The averaged function is expressed in terms of the Gauss hypergeometric function whereas the associated generating function is the so called Appell hypergeometric function . The Gauss hypergeometric function related

Delayed resonator (DR), which enables complete vibration suppression through loop delay tuning, has been extensively investigated as a linear active dynamic vibration absorber since its invention. Besides, the nonlinear high-static-low-dynamic stiffness (HSLDS) has been widely used in vibration isolators for broadband (yet incomplete) vibration reduction. This work combines the benefits of DR and the

In the present study, we introduce a high-order non-polynomial spline method designed for non-linear time-fractional reaction–diffusion equations with an initial singularity. The method utilizes the L2-1 scheme on a graded mesh to approximate the Caputo fractional derivative and employs a parametric quintic spline for discretizing the spatial variable. Our approach successfully tackles the impact of

In this paper, we propose inertial Halpern-type algorithms involving a quasi-monotone operator for approximating solutions of variational inequality problems which are fixed points of quasi-nonexpansive mappings in reflexive Banach spaces. We use Bregman distance functions to enhance the efficiency of our algorithms and obtain strong convergence results, even in cases where the Lipschitz constant of

This paper delves into the synchronization dynamics of fractional-order memristor Cohen–Grossberg neural network systems with time-varying delays at predefined times (PTS-MFCGNNs). Firstly, leveraging the concept of predefined-time stability, we devise a fractional-order controller, establish sufficient conditions for predefined-time synchronization, and achieve synchronization within the Cohen–Grossberg

In this study, we investigate a control problem involving a reaction–diffusion partial differential equation (PDE). Specifically, the focus is on optimizing the chemotherapy scheduling for brain tumor treatment to minimize the remaining tumor cells post-chemotherapy. Our findings establish that a bang-bang increasing function is the unique solution, affirming the MTD scheduling as the optimal chemotherapy

This paper achieves the synchronization of delayed neural networks (DNNs) considering aperiodic sampled-data control and communication delay. First of all, based on the master-slave DNNs with aperiodic sampling synchronization controller, a synchronization error system is constructed. Then, an augmented functional containing both the error state and its derivative is constructed. Compared with the

Luo et al. conjectured that for a tree with bipartition and , if a -connected bipartite graph with minimum degree at least , then has a subtree isomorphic to such that is -connected. Although this conjecture has been validated for spiders and caterpillars in cases where , and also for paths with odd order, its general applicability has remained an open question. In this paper, we establish the validity

Globally, there is a widespread awareness of poverty-related challenges. It's important to acknowledge that poverty is one of the key factors influencing prostitution. Addressing the rise in prostitution due to economic challenges is a major concern among the general public. In that scenario, many poor family girls/women were ready to downgrade their status for their family welfare and necessary needs

This article investigates the stabilization property for the modeled memristive bidirectional associative memory neural networks with time-varying delay when the faulty signals received from the fluctuated controller. The non-fragile output-feedback controller is taken into account to counteract the impact of gain perturbations to end up with robust fault-tolerant setup. To tackle the weak signals

The cell membrane has a layered structure, which separates the intracellular and extracellular ions for developing gradient electromagnetic field, and its flexible property enables the capacitance dependence on the shape deformation due to external stimuli. Therefore, piezoelectric membrane can be suitable to describe the biophysical characteristic of cell membrane and equivalent circuit approach becomes

To avoid solving a saddle-point system, in this paper, we study two-level Arrow–Hurwicz finite element methods for the steady bio-convection flows problem which is coupled by the steady Navier–Stokes equations and the steady advection–diffusion equation. Using the mini element to approximate the velocity, pressure, and the piecewise linear element to approximate the concentration, we use the linearized

The stochastic optimization of a nonlinear energy sink (NES) with a time-dependent stiffness is considered. The NES is linearly coupled to a main system. The optimization aims to find the stiffness properties of the NES that minimize the expected value of the velocity of the main system while accounting for the statistical distributions of the excitation amplitude and frequency. It is shown that the

This study addresses the problem of attack-compensated asynchronous output feedback control for stochastic switching systems with sojourn probability. Unlike traditional Markov/semi-Markov models that rely on transition probabilities, a novel switching rule is introduced that focuses on sojourn probability information associated with the target mode and sojourn time, which are easier to obtain than

Let be a graph and let denote the number of Laplacian eigenvalues of in the interval . For a tree T with diameter , Guo, Xue, and Liu proved that . In this paper, we provide a lower bound for when is a unicyclic graph, in terms of the diameter and girth of . Moreover, for the lollipop graph, under certain conditions on its diameter and girth, we give a formula for the exact value of .

This article addresses the challenge of achieving practically fast finite-time stabilization for stochastic constrained nonlinear systems, which are subject to both quantization effects and actuator dead zones. To tackle these issues, adaptive parameterization and partial control strategies are introduced with the aim of efficiently approximating and counteracting nonlinear disturbances. This approach

This paper investigates the problem of finite time prescribed performance control (PPC) for a number of nonlinear stochastic systems with asymmetric error constraint, unknown control directions, and actuator faults. Firstly, instead of introducing the performance constraint function in the Lyapunov function, a new asymmetric error conversion function (AECF) is presented, which can successfully constrain

Due to the existence of gaps or backlash, many mechanical systems can be simplified into piecewise linear models. The dynamic study on mechanical systems should be based on reliable mathematical models. So that it is very important to determine the contact point and separation point between the primary system and the auxiliary spring system (ASS) in a piecewise linear system. In most existing literature

In this article, we explore the general decay anti-synchronization (GDAS) and general decay anti-synchronization (GDHAS) of derivative coupled delayed memristive neural networks (DCDMNNs) with constant and delayed state coupling, respectively. To begin with, on account of the definitions of -type function as well as -type stability, we present the GDAS and GDHAS concepts for the considered DCDMNNs

In this article, a kind of second-order neural networks with variable coefficients and distributed delays are discussed. At first, new lemmas about fixed/preassigned-time synchronization for such system are respectively constructed. Then, some novel criteria are given to get fixed/preassigned-time synchronization for such delayed system based on the these lemmas. Unlike feedback controllers are used

In this paper, an extended (3+1)-dimensional nonlinear Schrödinger equation is studied. By using similarity transformation, some exact solutions of this equation are obtained, which include soliton solutions and periodic function solutions, its nonlinear spatial modulation and external potential are affected by time and space. Based on the solution obtained previously, some figures are displayed.

This work presents an Ambrosetti–Prodi alternative for functional problems composed of a fully third-order differential equation with two types of functional boundary conditions. The discussion of existence and non-existence of solution is obtained in a more general case, and the multiplicity of solution is done with restrictive boundary conditions-

In this article, we propose a dynamic event-triggered neuro-optimal control scheme (DETNOC) for uncertain nonlinear systems subject to unknown dead-zone and disturbances through the design of a composite control law. An integral sliding mode-based discontinuous control law is utilized to compensate for the effects of unknown dead-zone, disturbance, and a component of uncertainties. As a result, a system

In this paper, we introduce some novel concepts within the realm of fuzzy bipolar metric spaces, namely ()-contractive type covariant mappings and contravariant mappings, and ()-contractive type covariant mappings. We establish some fixed point theorems that demonstrate both the existence and uniqueness of fixed points for ()-contractive type covariant mappings and contravariant mappings, and for ()-contractive

In this paper, we investigate the control and dynamic behavior of the inverted pendulum system with time delay under fractional Gaussian noise excitation. For H=1/2 and H, we analyze the stochastic dynamic characteristics of the system under Hopf bifurcation, utilizing time delay and noise intensity as bifurcation parameters, and validate the theoretical conclusions through numerical simulations. We

This paper considers a Belousov–Zhabotinskii reaction–diffusion system with spatio-temporal delay. The spatio-temporal delay is modeled as the convolution of with a kernel function , where . By constructing an auxiliary system, applying Schauder’s fixed point theorem, and using a limiting argument, we demonstrate that the model admits non-negative traveling wave solutions connecting the equilibrium

In this paper, we deal with numerical approximations for solving the Black–Scholes Partial Differential Equation (PDE) for European and American options pricing with local volatility. This PDE is well-known to be degenerated. Local volatility model is a model where the volatility depends locally of both stock price and time. In contrast to constant volatility or time-dependent volatility models for

– In this paper, we consider the following stationary two-species chemotaxis-competition system with signal-dependent diffusion and sensitivity in a bounded smooth domain , where are positive constants, and with for all . Since there does not exist an immediate change variable that transforms (0.1) into a semilinear system when (0.1) is considered with being arbitrary functions in , this makes the